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4024/21 May/Jun 2022, Question 10: Describing Transformations

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 5 marks

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The question, in short

Using a grid with triangles A, B and C, describe the transformation mapping A to B, find the matrix mapping A to C, and draw triangle D from an enlargement of A.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Describe fully the single transformation that takes triangle A onto triangle B.

  1. 1Each vertex moves 4 left and 3 up, e.g. (1, 1) → (−3, 4)
  2. 2Translation by column vector (−4, 3)

AnswerTranslation column vector (−4, 3)

Part (b) · 1 mark

Find the matrix for the transformation mapping triangle A onto triangle C.

  1. 1(1, 1) → (−1, 1) and (3, 1) → (−3, 1): a reflection in the y-axis
  2. 2Matrix with rows (−1, 0) and (0, 1)

Answermatrix with rows (−1, 0) and (0, 1)

Part (c) · 2 marks

Draw triangle D, the image of A under enlargement centre (2, 3) scale factor 3.

  1. 1Vector from centre (2, 3) to each vertex of A, multiplied by 3
  2. 2(1, 1): 2 + 3(−1) = −1, 3 + 3(−2) = −3 → (−1, −3)
  3. 3(1, 2) → (−1, 0) and (3, 1) → (5, −3)
  4. 4Draw triangle D with vertices (−1, 0), (−1, −3), (5, −3)

AnswerTriangle at (−1, 0), (−1, −3), (5, −3)

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Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 10.
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